Equivalent definitions for the measurability of a multivariate function and Filippov's lemma

Adam Idzik. "Equivalent definitions for the measurability of a multivariate function and Filippov's lemma." Mathematica Applicanda 7.14 (1979): null. <http://eudml.org/doc/293445>.

@article{AdamIdzik1979,
abstract = {From the text: "In the many papers in which the concept of measurability of a multivariate function arises, the authors usually formulate one definition of measurability and ignore its connections with other definitions. Assuming that the space, in which the values of the multivariate function lie, which admits only a closed set, is metric and compact we prove that all well-known definitions of measurability of multivariate functions are equivalent. "A. F. Filippov's lemma was first formulated in 1959 [Vestnik Moskov. Univ. Ser. Mat. Meh. Astr. Fiz. Him. 1959, no. 2, 25–32; MR0122650] and was later generalized by many others, in particular by W. Furakawa [Ann. Math. Statist. 43 (1972), 1612–1622; MR0371418], C. J. Himmelberg [Fund. Math. 87 (1975), 53–72; MR0367142] and C. Olech [Bull. Acad. Polon Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 317–321; MR0199338]. Using various definitions of measurability of a multivariate function (whose equivalence we prove beforehand) we introduce two theorems on the existence of a measurable implicit function. These theorems generalize Furakawa's theorem [op. cit.] which is a reformulation of Olech's theorem [op. cit.] for Borel measurability.''},
author = {Adam Idzik},
journal = {Mathematica Applicanda},
keywords = {Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence},
language = {eng},
number = {14},
pages = {null},
title = {Equivalent definitions for the measurability of a multivariate function and Filippov's lemma},
url = {http://eudml.org/doc/293445},
volume = {7},
year = {1979},
}

TY - JOUR
AU - Adam Idzik
TI - Equivalent definitions for the measurability of a multivariate function and Filippov's lemma
JO - Mathematica Applicanda
PY - 1979
VL - 7
IS - 14
SP - null
AB - From the text: "In the many papers in which the concept of measurability of a multivariate function arises, the authors usually formulate one definition of measurability and ignore its connections with other definitions. Assuming that the space, in which the values of the multivariate function lie, which admits only a closed set, is metric and compact we prove that all well-known definitions of measurability of multivariate functions are equivalent. "A. F. Filippov's lemma was first formulated in 1959 [Vestnik Moskov. Univ. Ser. Mat. Meh. Astr. Fiz. Him. 1959, no. 2, 25–32; MR0122650] and was later generalized by many others, in particular by W. Furakawa [Ann. Math. Statist. 43 (1972), 1612–1622; MR0371418], C. J. Himmelberg [Fund. Math. 87 (1975), 53–72; MR0367142] and C. Olech [Bull. Acad. Polon Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 317–321; MR0199338]. Using various definitions of measurability of a multivariate function (whose equivalence we prove beforehand) we introduce two theorems on the existence of a measurable implicit function. These theorems generalize Furakawa's theorem [op. cit.] which is a reformulation of Olech's theorem [op. cit.] for Borel measurability.''
LA - eng
KW - Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
UR - http://eudml.org/doc/293445
ER -